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We theoretically investigated spectrally uncorrelated biphotons generated ina counter-propagating spontaneous parametric downconversion (CP-SPDC) fromperiodically poled MTiOXO4 (M = K, Rb, Cs; X = P, As) crystals. By numericalcalculation, it was found that the five crystals from the KTP family can beused to generate heralded single photons with high spectral purity and widetunability. Under the type-0 phase-matching condition, the purity at 1550 nmwas between 0.91 and 0.92, and the purity can be maintained over 0.90 from 1500nm to 2000 nm wavelength. Under the type-II phase-matching condition, thepurity at 1550 nm was 0.96, 0.97, 0.97, 0.98, and 0.98 for PPKTP, PPRTP, PPKTA,PPRTA, and PPCTA, respectively; furthermore, the purity can be kept over 0.96for more than 600 nm wavelength range. We also simulated the Hong-Ou-Mandelinterference between independent photon sources for PPRTP crystals at 1550 nm,and interference visibility was 92% (97%) under type-0 (type-II) phase-matchingcondition. This study may provide spectrally pure narrowband single-photonsources for quantum memories and quantum networks at telecom wavelengths.

Counter-propagating spectrally uncorrelated biphotons at 1550 nm generated from periodically poled MTiOXO4 (M = K, Rb, Cs; X = P, As)